Discussion on “Interaction Effects in Marine Seismic Source Arrays”*

Abstract

1980) published the results of a theoretical work which purported to deal with the effects of interaction (mutual coupling) in marine seismic source arrays. The purpose of this note is to show that Sinclair and Bhattacharya did not deal with the problem of interaction. In fact, they dealt with a problem, which was first studied by Stenzel (1930), namely the determination of the " directivity factor" of arrays of point sources.In order to show that the concept of the directivity factor of an array is different from the concept of interaction between an array of sources we will review briefly the two concepts.Consider a linear array of a number of identical air bubbles pulsating with small volumetric displacement. The motion of one air bubble in the absence of the other air bubbles can be described (Safar 1976) by the following equation:where Mr and R, are the radiation mass and resistance of the pulsating air bubble, v and V, are the air bubble instantaneous and equilibrium volumes, C is the air bubble compliance, and R 1 is the damping resistance due to heat losses.In the presence of mutual coupling between the air bubbles, the motion of each air bubble is described bywhere ML and RL are the radiation mass and resistance of each air-bubble in the presence of mutual coupling (interaction).